Researchers used complete genome sequencing of 15 father-child pairs to tally the total number of new mutations inherited from each father. The age of the father and total number of new mutations are provided in the table below.

Father's Age (years) 18 20 19 22 24 24 24 25 28 29 30 32 37 36 34

Number of New Mutations 41 39 49 50 54 55 61 57 52 54 57 52 54 57 61

Conduct a linear regression analysis of the data using the father's age as the explanatory variable (x) and the number of new mutations as the response variable (y).

Examine the scatterplot with the regression line and diagnostic plots for the independent and dependent variables. For each plot say what the plot shows for this dataset and what conclusions (if any) can be drawn.